Comparing Quantities Test

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Comparing Quantities Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

A person sold two almirah for Rs. 1,980 each. On one he gained 10% while on other he lost 10%. In the bargain he

A
gained 2%

B
lost 1%

C
gained 10%

D
none of these

Solution

S.P of two almirah=$$1980\times 2=Rs.3960$$
If he gained 10% then the cost price of that almirah=$$\frac{100}{100+10}\times 1980=Rs.1800$$
If he lost 10% then the cost price of that almirah=$$\frac{90}{100}\times 1980=Rs. 2200$$
C.P of two almirah=$$1800+2200=Rs.4000$$
$$\therefore loss=4000-3960=Rs.40$$
Loss %=$$\frac{loss}{ C.P}\times 100=\frac{40}{4000}\times 100=1$$%
Question 2
1 / -0

If the CP is $$96\%$$ of the SP, then what is the profit percentage?

A
$$\displaystyle4\frac{1}{6}\%$$

B
$$\displaystyle4\frac{1}{3}\%$$

C
$$\displaystyle4\frac{1}{2}\%$$

D
5%

Solution

Let $$SP=Rs.100$$

$$\therefore CP=Rs.96$$

Profit $$=100-96=4$$

Profit percent $$\displaystyle=\left(\frac{Profit}{CP}\times100\right)\%$$

$$=\left(\dfrac{4}{96}\times100\right)\%$$

$$=\dfrac{25}{6}\%$$

$$=4\dfrac{1}{6}\%$$
Question 3
1 / -0

A dealer sold three-fourth of the articles at a gain of $$20\%$$ and the remaining at CP. Find the gain earned by him in the whole transaction.

A
$$10\%$$

B
$$12\%$$

C
$$15\%$$

D
$$16\%$$

Solution

Let the CP of whole be x.

CP of $$\displaystyle\frac{3}{4}th=\frac{3x}{4}$$

CP of $$\displaystyle\frac{1}{4}th=\frac{x}{4}$$

Total $$\displaystyle SP=\left(120\%\:of\:\frac{3x}{4}+\frac{x}{4}\right)=\left(\frac{120}{100}\times\frac{3x}{4}+\frac{x}{4}\right)=\frac{23x}{20}$$

Gain $$\displaystyle=SP-CP=\frac{23x}{20}-x=\frac{23x-20x}{20}=\frac{3x}{20}$$

Gain% $$\displaystyle=\left(\frac{3x}{20}\times\frac{1}{x}\times100\right)=15\%$$
Question 4
1 / -0

By selling a suitcase for Rs. 570, a man loses 5%. At what price must he sell it to gain 5%?

A
Rs. 630

B
Rs. 650

C
Rs. 580

D
Rs. 620

Solution

Selling Price=Rs.570
Loss =5%
$$\therefore C.P =\frac{100}{100-loss\%}\times S.P$$
$$\Rightarrow \frac{100}{95}\times 570=Rs.600$$
Now C.P of the suitcase=600
Gain%=5%
$$\therefore S.P=\frac{100+gain \%}{100} \times C.P$$
$$=\frac{105}{100}\times 600=Rs.630$$
Hence he sell Rs.630 to gain 5%.
Question 5
1 / -0

If the MP is $$30\%$$ above CP and a discount of $$10\%$$ is given for cash payments, what is the profit?

A
$$10\%$$

B
$$15.5\%$$

C
$$17\%$$

D
$$18.5\%$$

Solution

Now according to question:

Let, $$CP = 100$$

$$MP = 100+30\%\ of\ 100\\\ \ \ \ \ \ =Rs\ 130$$

$$Discount = 10\%\ of\ MP \\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =Rs\ 13$$

$$SP = MP - Discount \\= 130 - 13 \\=Rs\ 117$$

$$Profit = SP - CP = \\117 - 100 \\= Rs\ 17$$

Hence,
$$Gain\ \% =\dfrac{gain}{CP}\times 100\\\ \ \ \ \ \ \ \ \ \ \ \ = 17\%$$
Question 6
1 / -0

The CP of $$15$$ articles is equal to the sale price of $$12$$ articles. The profit $$\%$$ is

A
$$25\%$$

B
$$30\%$$

C
$$\displaystyle33\frac{1}{3}\%$$

D
$$50\%$$

Solution

SP of 12 items $$=15$$

SP of 15 Items $$\displaystyle=\frac{15}{12}\times15=\frac{75}{4}=18.75$$

$$\therefore$$ Profit $$=18.75-15=3.75$$
Profit for 115 $$=3.75$$

Profit for 100 $$\displaystyle=\frac{3.75}{15}\times100=25\%$$
Question 7
1 / -0

The CP of an article is $$64\%$$ of the MP. If there is a discount of $$12\%$$ on the article, what is the profit percent?

A
$$37.5\%$$

B
$$48\%$$

C
$$50.5\%$$

D
$$52\%$$

Solution

Let the MP be 100.
Then, the CP is 64.
Discount is 12%. Hence, $$SP=100-12=88$$. Therefore,
$$Profit=88-64=24$$
For 64, the profit is 24.

For 100, the profit is $$\displaystyle\frac{24}{64}\times100=37.5\%$$.
Question 8
1 / -0

X, Y and Z are the three sums of money. X is the simple interest on Y, and Y is the simple interest on Z. The rate percent per year and the time in years being the same in each case. Which one of the following relations in X, Y, Z is correct?

A
$$XYZ=100$$

B
$$Y^2=XZ$$

C
$$Z^2=XY$$

D
$$X^2=YZ$$

Solution

b'$$\displaystyle X=\frac{Y\times r\times t}{100}$$ and $$\displaystyle Y=\frac{Z\times r\times t}{100}$$

$$\displaystyle\frac{X}{Y}=\frac{Y}{Z}$$ i.e., $$Y^2=XZ$$'
Question 9
1 / -0

A fruit seller bought fruits for $$666$$ and sold it for $$777$$. His gain percent is nearly

A
$$12\%$$

B
$$\displaystyle12\frac{1}{4}\%$$

C
$$\displaystyle13\frac{1}{3}\%$$

D
$$\displaystyle16\frac{2}{3}\%$$

Solution

$$SP=777$$
$$CP=666$$
Profit $$=111$$
For 666, profit $$=111$$

For 100, profit $$\displaystyle=\frac{111}{666}\times100=16\frac{2}{3}\%$$
Question 10
1 / -0

If the list price of a book is reduced by Rs 5, a person can buy 5 more books for Rs 300. Then the original cost of the book is

A
Rs 15

B
Rs 20

C
Rs 25

D
Rs 30

Solution

Let the original list price of the book be=Rs x
Original number of books purchased=$$\frac { 300 }{ x } $$
When the price of the book is reduced by 5
New Number of books purchased will be=$$\frac { 300 }{ x-5 } $$
New number of books purchased-Original number of books purchased=5
$$\therefore \frac { 300 }{ x-5 } -\frac { 300 }{ x } =5$$
$$\Rightarrow \frac { 300x-300x+1500 }{ x\left( x-5 \right) } =5$$
$$\Rightarrow { x }^{ 2 }-5x=300$$
$$\Rightarrow { x }^{ 2 }-20x+15x-300=0$$
$$\Rightarrow { x }\left( x-20 \right) +15\left( x-20 \right) =0$$
$$\Rightarrow \left( x-20 \right) \left( x+15 \right) =0$$
$$\Rightarrow x-20=0\quad or\quad x+15=0$$
$$\Rightarrow x=20\quad or\quad x=-15$$
$$\therefore x=20$$
the original cost of book is Rs 20

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Comparing Quantities Test - 37

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Comparing Quantities Test - 37

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SHARING IS CARING

Question 1

gained 2%

lost 1%

gained 10%

none of these

Solution

Question 2

$$\displaystyle4\frac{1}{6}\%$$

$$\displaystyle4\frac{1}{3}\%$$

$$\displaystyle4\frac{1}{2}\%$$

5%

Solution

Question 3

$$10\%$$

$$12\%$$

$$15\%$$

$$16\%$$

Solution

Question 4

Rs. 630

Rs. 650

Rs. 580

Rs. 620

Solution

Question 5

$$10\%$$

$$15.5\%$$

$$17\%$$

$$18.5\%$$

Solution

Question 6

$$25\%$$

$$30\%$$

$$\displaystyle33\frac{1}{3}\%$$

$$50\%$$

Solution

Question 7

$$37.5\%$$

$$48\%$$

$$50.5\%$$

$$52\%$$

Solution

Question 8

$$XYZ=100$$

$$Y^2=XZ$$

$$Z^2=XY$$

$$X^2=YZ$$

Solution

Question 9

$$12\%$$

$$\displaystyle12\frac{1}{4}\%$$

$$\displaystyle13\frac{1}{3}\%$$

$$\displaystyle16\frac{2}{3}\%$$

Solution

Question 10

Rs 15

Rs 20

Rs 25

Rs 30

Solution

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